Water distribution systems convey drinking water from treatment plant and make available to consumers’ taps. It consists of essential components like pipes, valves, pumps, tanks and reservoirs etc. The main concern in the working of a water distribution system is to assure customer demands under a choice of quantity and quality throughout the complete life span for the probable loading situations. However, in some cases, the existing infrastructure may not be adequate to meet the customer’s requirements. In such cases, system modeling plays an important role in proper management of water supply systems. In present scenario, modeling plays a significant task in appropriate execution of water distribution system. From the angle of taking management decisions valve throttling control and pumps speed control are very important. These operational problems can be addressed by manual control or by automatic control. The problem is the use of manual controls that slow down the effectiveness of the system. It reduces the efficiency of operation of valve or pump. To improve the efficiency of such water distribution systems, an automatic control based technology has been developed that links the operation of the variable speed pump control or valve throttling control. By employing an automatic control, the pump can adjust its speed at all times to meet the actual flow requirements of each load served. In case of real system design Simulink is the most widely used tool. Commercial software package Matlab/Simulink used for creation of WDS model. The goal was to produce a model that could numerically analyze the dynamic performance of a water distribution system. A Comparison of single platform methodology (Simulink based control) and double platform methodology (Matlab and EPANET based control) has been done. Nonlinear Dynamic Inversion (DI) Control system model is developed for WDS model in Matlab/Simulink environment. Controller gain parameters are the very important value in control prospective. If the controller gain parameters are chosen incorrectly, the controlled process input can be unstable, i.e. its output diverges, with or without oscillation Tuning is the adjustment of control parameters (gains) to the optimum values for the desired control response. There are several methods for tuning controller like manual tuning (Trial and error procedure), Ziegler-Nichols method, Output Constraint Tuning (OCT) etc. Establishment of a pump operational policy by which all the reservoirs can be fed simultaneously to meet their requirements without creating undue transients. Tune the gain of DI controllers by different tuning methods and evaluate the best tuning method on the basis of controller performance. Development of meaningful additional objective is search of lower bound pump speed on the basis of control time or settling time. To bring the pump speeds in feasible range, application of constraint in pumps speed is introduced. The magnitude of constraints can be found using Monte Carlo methods. Monte Carlo methods are frequently used in simulating physical and mathematical systems. This method may be the most commonly applied statistical method in engineering and science disciplines. Another benefit is providing increased confidence that a model is robust using Monte Carlo testing. Model development for generalized control system for water distribution network provides the simplification needed for the simulation of large systems. Model development is based on the study of symmetric and non symmetric small, irregular networks, as well as large, regular and open bifurcating water distribution system. The problem considered in this section is that of flow dynamics in simple to complex, regular network which bifurcates in the form of a branching tree. In addition the control application of the flow network is investigated using valves as the manipulated variables to control branch flow rates. Communication between the network hydraulics coming from EPANET and control algorithm develop on Matlab (Programming Language) can be generalized with the help of development of general purpose control algorithm model.

In this thesis we consider the calibration of models based on Lévy processes to option prices observed in some market. This means that we choose the parameters of the option pricing models such that the prices calculated using the models correspond as closely as possible to these option prices. We demonstrate the ability of relatively simple Lévy option pricing models to nearly perfectly replicate option prices observed in nancial markets. We speci cally consider calibrating option pricing models to barrier option prices and we demonstrate that the option prices obtained under one model can be very accurately replicated using another. Various types of calibration are considered in the thesis. We calibrate a wide range of Lévy option pricing models to option price data. We con- sider exponential Lévy models under which the log-return process of the stock is assumed to follow a Lévy process. We also consider linear Lévy models; under these models the stock price itself follows a Lévy process. Further, we consider time changed models. Under these models time does not pass at a constant rate, but follows some non-decreasing Lévy process. We model the passage of time using the lognormal, Pareto and gamma processes. In the context of time changed models we consider linear as well as exponential models. The normal inverse Gaussian (N IG) model plays an important role in the thesis. The numerical problems associated with the N IG distribution are explored and we propose ways of circumventing these problems. Parameter estimation for this distribution is discussed in detail. Changes of measure play a central role in option pricing. We discuss two well-known changes of measure; the Esscher transform and the mean correcting martingale measure. We also propose a generalisation of the latter and we consider the use of the resulting measure in the calculation of arbitrage free option prices under exponential Lévy models. / PhD (Risk Analysis), North-West University, Potchefstroom Campus, 2015

In this thesis we consider the calibration of models based on Lévy processes to option prices observed in some market. This means that we choose the parameters of the option pricing models such that the prices calculated using the models correspond as closely as possible to these option prices. We demonstrate the ability of relatively simple Lévy option pricing models to nearly perfectly replicate option prices observed in nancial markets. We speci cally consider calibrating option pricing models to barrier option prices and we demonstrate that the option prices obtained under one model can be very accurately replicated using another. Various types of calibration are considered in the thesis. We calibrate a wide range of Lévy option pricing models to option price data. We con- sider exponential Lévy models under which the log-return process of the stock is assumed to follow a Lévy process. We also consider linear Lévy models; under these models the stock price itself follows a Lévy process. Further, we consider time changed models. Under these models time does not pass at a constant rate, but follows some non-decreasing Lévy process. We model the passage of time using the lognormal, Pareto and gamma processes. In the context of time changed models we consider linear as well as exponential models. The normal inverse Gaussian (N IG) model plays an important role in the thesis. The numerical problems associated with the N IG distribution are explored and we propose ways of circumventing these problems. Parameter estimation for this distribution is discussed in detail. Changes of measure play a central role in option pricing. We discuss two well-known changes of measure; the Esscher transform and the mean correcting martingale measure. We also propose a generalisation of the latter and we consider the use of the resulting measure in the calculation of arbitrage free option prices under exponential Lévy models. / PhD (Risk Analysis), North-West University, Potchefstroom Campus, 2015

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Master of Science / Department of Statistics / Leigh Murray / The southern root-knot nematode (SRKN) and the weedy perennials, yellow nutsedge (YNS) and purple nutsedge (PNS) are simultaneously occurring pests in the irrigated agricultural soils of southern New Mexico. Previous research has very well characterized SRKN, YNS and PNS as a mutually-beneficial pest complex and has revealed their enhanced population growth and survival when they occur together. The density of nutsedge in a field could be used as a predictor of SRKN juveniles in the soil. In addition to SRKN, which is the most harmful of the plant parasitic nematodes, in southern New Mexico, other species or categories of nematodes could be identified and counted. Some of them are not as damaging to the plant as SRKN, and some of them may be essential for soil health. The nematode species could be grouped into categories according to trophic level (what nematodes eat) and herbivore feeding behavior (how herbivore nematodes eat). Subsequently, three ratios of counts were calculated for trophic level and for feeding behavior level to investigate the soil nematode community structure. These proportions were modeled as functions of the weed hosts YNS and PNS by generalized linear regression models using the logit link function and three probability distributions: the Binomial, Zero Inflated Binomial (ZIB) and Binomial Hurdle (BH). The latter two were used to account for potential high proportions of zeros in the data. The SAS NLMIXED procedure was used to fit models for each of the six sampling dates (May, July and September) over the two years of the alfalfa study. General results showed that the Binomial pmf generally provided the best fit, indicating lower zero-inflation than expected. Importance of YNS and PNS predictors varied over time and the different ratios. Specific results illustrate the differences in estimated probabilities between Binomial, ZIB and BH distributions as YNS counts increase for two selected ratios.

The generalized gamma (GG) distribution is an important model that has proven to be very flexible in practice for modeling data from several areas. This model has important sub-models, such as the Weibull, gamma, lognormal, Nakagami-m distributions, among others. In this work, our main objective is to develop different estimation procedures for the unknown parameters of the generalized gamma distribution and related models (Nakagami-m and gamma), considering both classical and Bayesian approaches. Under the Bayesian approach, we provide in a simple way necessary and sufficient conditions to check whether or not objective priors lead proper posterior distributions for the Nakagami, gamma, and GG distributions. As a result, one can easily check if the obtained posterior is proper or improper directly looking at the behavior of the improper prior. These theorems are applied to different objective priors such as Jeffreyss rule, Jeffreys prior, maximal data information prior and reference priors. Simulation studies were conducted to investigate the performance of the Bayes estimators. Moreover, maximum a posteriori (MAP) estimators for the Nakagami and gamma distribution that have simple closed-form expressions are proposed Numerical results demonstrate that the MAP estimators outperform the existing estimation procedures and produce almost unbiased estimates for the fading parameter even for a small sample size. Finally, a new lifetime distribution that is expressed as a two-component mixture of the GG distribution is presented. / A distribuição gama Generalizada (GG) possui um papel fundamental para modelar dados em diversas áreas. Tal distribuição possui como casos particulares importantes distribuições, tais como, Weibull, Gama, lognormal, Nakagami-m, dentre outras. Nesta tese, tem-se como objetivo principal, considerando as abordagens clássica e Bayesiana, desenvolver diferentes procedimentos de estimação para os parâmetros da distribuição gama generalizada e de alguns dos seus casos particulares dentre eles as distribuições Nakagami-m e Gama. Do ponto de vista Bayesiano, iremos propor de forma simples, condições suficientes e necessárias para verificar se diferentes distribuições a priori não-informativas impróprias conduzem a distribuições posteriori próprias. Tais resultados são apresentados para as distribuições Nakagami-m, gama e gama generalizada. Assim, com a criação de novas prioris não-informativas, para tais modelos, futuros pesquisadores poderão utilizar nossos resultados para verificar se as distribuições a posteriori obtidas são impróprias ou não. Aplicações dos teoremas propostos são apresentados em diferentes prioris objetivas, tais como, a regra de Jeffreys, priori Jeffreys, priori maximal data information e prioris de referência. Iremos também realizar estudos de simulação para investigar a influência destas prioris nas estimativas a posteriori. Além disso, são propostos estimadores de máxima a posteriori em forma fechada para as distribuições Nakagami-m e Gama. Por meio de estudos de simulação verificamos que tais estimadores superam os procedimentos de estimação existentes e produzem estimativas quase não-viciadas para os parâmetros de interesse. Por fim, apresentamos uma nova distribuição obtida considerando um modelo de mistura de distribuições gama generalizada.

Matrix variate skew elliptically contoured distributions generalize several classes of important distributions. This paper defines and explores matrix variate skew elliptically contoured distributions. In particular, we discuss two stochastic representations of the matrix variate skew elliptically contoured distributions.

Distribution of profit and other capital in commercial capital company Abstract The right to receive dividends is one of the fundamental rights of each shareholder of a capital company. Even though it stems from the very nature of a capital company that its shareholders will often wish to exercise solely their right to receive dividends, and not their right to participate in the management of the company, it is obvious that even capital companies may be established for purposes other than that of achieving profit alone. At the same time, companies, which were established solely for the purpose of achieving profit may wish to postpone the realization of profit for various reasons. Therefore, it is important for the law to be flexible enough to accommodate these needs while still providing adequate protection to creditors and minority shareholders of the company. Generally speaking, the Czech legal regulations governing the distribution of profit and other capital strike the balance between these competing interests fairly well. On the other hand, the rules contained in the Business Corporations Act are surrounded by a number of interpretational problems and uncertainties, e.g. because the applicability of the Czech Supreme Court jurisprudence issued in relation to the former Commercial Code has been called...

In this thesis we present some related problems about the renewal processes. More precisely, let $gamma_{t}$ be the residual life at time $t$ of the renewal process $A={A(t),t geq 0}$, $F$ be the common distribution function of the inter-arrival times. Under suitable conditions, we prove that if $Var(gamma_{t})=E^2(gamma_{t})-E(gamma_{t}),forall t=0,1 ho,2 ho,3 ho,... $, then $F$ will be geometrically distributed under the assumption $F$ is discrete. We also discuss the tails of random sums for the renewal process. We prove that the $k$ power of random sum is always new worse than used ($NWU$).

Ce travail est lié au système de protection des réseaux de distribution. Les réseaux radiaux dedistribution peuvent être protégés simplement par une protection placée en tête du départ. Maisl'exploitation future des réseaux de distribution, qui se transforment en réseaux intelligents,flexibles et adaptatifs, va sûrement nécessiter une protégeabilité plus complexe. Parconséquent, un nouveau plan de protection pourrait être nécessaire afin d’augmenter la fiabilitédu réseau de distribution et le taux de productions décentralisées. Il pourrait inclure plusieursprotections déployées sur un départ. Le but principal de ce travail est d'étudier comment lesprotections pourraient agir (sur quel genre de grandeurs les protections reposeront, quellecoordination faut-il choisir) et d'analyser les limites de ces nouvelles protections. En déployantplusieurs protections qui divisent le départ en des zones plus petites, le plan de protectionproposé, reposant sur une formulation modifié et optimisée, proche de celle des protections dedistance classiques, déconnectera ainsi moins de consommateurs et de producteurs lors del’apparition de défauts. Cela devrait réduire le temps de coupures brèves et de diminuerl'énergie non fournie. Ce manuscrit présente une solution pour les réseaux HTA radiaux faceaux défauts monophasés. / This work is related to the protection system of distribution networks. Radial MV distributiongrids can be protected by a single protection relay located at the beginning of the feeder. Butthe future operation mode of distribution grids turning into Smart Grids should impose morecomplex operations. Therefore a more advanced protection scheme could be needed, in orderto improve the reliability of the distribution network and to enhance the DG interconnection. Itcould include several protection relays in series on a same MV feeder. The main purpose of thiswork is to investigate how the protection relays could work (on which measurements should theprotection decisions be based, how to coordinate the relays without communication) andanalyze the limits of such new protection schemes. Since the goal is to insert severalprotections that divide the grid into smaller sections, the proposed protection system, based onan adapted and optimized formula, inspired by distance relays algorithm, would thereforedisconnect fewer loads and producers when faults occur in the MV network. This should reducethe clearing operation time and Energy Not Supplied criteria. This paper presents a solution fora radial MV grid facing single-phased faults.